Microscopic modeling of tunable graphene-based terahertz Landau-level lasers

Abstract

In the presence of strong magnetic fields the electronic bandstructure of graphene drastically changes. The Dirac cone collapses into discrete non-equidistant Landau levels, which can be externally tuned by changing the magnetic field. In contrast to conventional materials, specific Landau levels are selectively addressable using circularly polarized light. Exploiting these unique properties, we propose the design of a tunable laser operating in the technologically promising terahertz spectral range. To uncover the many-particle physics behind the emission of light, we perform a fully quantum mechanical investigation of the non-equilibrium dynamics of electrons, phonons, and photons in optically pumped Landau-quantized graphene embedded into an optical cavity. The gained microscopic insights allow us to predict optimal experimental conditions to realize a technologically promising terahertz laser.The terahertz (THz) regime of the electromagnetic spectrum can be exploited in a wide range of applications including medical diagnostics, atmosphere and space science as well as security and information technology [1][2][3][4]. Although THz research has progressed significantly in the last 20 years, the transition from laboratory demonstration to practical environment has occurred slowly and only for some niche applications. The largest challenge is the lack of adequate, tunable THz radiation sources. In 1986, H. Aoki proposed to design Landau level (LL) lasers exploiting the discreteness of LLs in two-dimensional electron gases [5]. Here, the energetic LL spacing and thus the possible laser frequency can be externally tuned through the magnetic field. The challenge for the realization of such a laser is to obtain a stable population inversion, i.e. a larger carrier occupation within an energetically higher LL. Since conventional semiconductors exhibit an equidistant spectrum of LLs, strong Coulomb scattering acts in favor of an equilibrium Fermi-Dirac distribution and strongly counteracts the build-up of a population inversion. In contrast, graphene as a two-dimensional material with a linear dispersion exhibits a non-equidistant LL separation offering entirely different conditions for many-particle processes [6][7][8]. Exploiting these remarkable properties of Landauquantized graphene, we propose an experimentally accessible scenario to achieve continuous wave lasing with tunable frequencies in the technologically promising terahertz spectral regime. The non-equidistant arrangement of energy levels [9,10] combined with selection rules for circularly polarized light, allow to selectively address individual inter-LL * samuel.brem@physik.tu-berlin.de Figure 1. Laser scheme. Sketch of the energetically lowest Landau levels in graphene embedded in an optical cavity. (A) The linearly polarized optical pump field induces transitions l = −3 → +2 and l = −2 → +3 (yellow arrows), which results in a population inversion between l = +1 and l = +2 in the conduction band and l = −1 and l = −2 in the valance band.(B) The emission o...

Suppressed Auger scattering and tunable light emission of Landau-quantized massless Kane electrons

“…1b). However, to the best of our knowledge, no cyclotron emission, let alone the Landau level laser based on graphene, has been reported so far, despite pertinent theoretical predictions and numerous experimental attempts 10,[20][21][22][23][24][25][26] .…”

Nonperturbative model for optical response under intense periodic fields with application to graphene in a strong perpendicular magnetic field

“…Recent studies of the nonlinear responses have been extended to wavelengths in the infrared. [2][3][4][5][6][7] A huge optical susceptibility is predicted by Yao and Belyanin 3,4 and confirmed by the four wave mixing (FWM) experiments of König-Otto et al in the far infrared. 5 Proposed applications for graphene-based photonics include the generation of entangled photons, 8 an all-optical switch, 9 tunable lasers, 6 the dynamic control of coherent pulses, 10 and the demonstration of optical bistability and optical multistability.…”

“…[2][3][4][5][6][7] A huge optical susceptibility is predicted by Yao and Belyanin 3,4 and confirmed by the four wave mixing (FWM) experiments of König-Otto et al in the far infrared. 5 Proposed applications for graphene-based photonics include the generation of entangled photons, 8 an all-optical switch, 9 tunable lasers, 6 the dynamic control of coherent pulses, 10 and the demonstration of optical bistability and optical multistability. 11,12 Theoretically, optical nonlinearities are mostly studied in an equation-of-motion framework, where solutions of the dynamical equations can be obtained in the rotating wave approximation (RWA) 3,4 or in perturbation method.…”

Electrically pumped graphene-based Landau-level laser

“…Due to the relativistic properties of low-energy electrons in graphene, the spacing between its lowest LLs is extremely large compared to conventional materials. Magnetic fields of a few Tesla give rise to LL transition energies ranging from the terahertz (THz) up to the far-infrared spectral ranges, which makes Landau-quantized graphene a highly promising material for the realization of tunable THz emitters and absorbers [6][7][8][9][10].…”

“…In previous work [10] we have shown that the remarkable properties of Landau-quantized graphene can be exploited to achieve continuous-wave lasing with an optically pumped population inversion (PI) between neighboring LLs. However, the optical excitation is highly challenging since one has to selectively address single LLs with energetic separations of a few tens of meV.…”